Question

Suppose that the total cost (in dollars) for a product is given by C(x) = 1300 + 190 ln(2x + 1) where x is the number of units produced. (a) Find the marginal cost function, MC. MC = (b) Find the total cost of producing 170 units. (round to 2 decimal places.) (c) Find the marginal cost when 170 units are produced. (round to 2 decimal places.)

Answer 1

The marginal cost function is obtained by taking the derivative of the total cost function. To find the total cost of producing 170 units and the marginal cost when 170 units are produced, simply substitute x = 170 into the respective functions.

Step-by-step explanation:

The marginal cost function is the derivative of the total cost function. So, to find the marginal cost function, we need to find the derivative of C(x). The derivative of 1300 is 0, and the derivative of 190 ln(2x + 1) is 190 * (1 / (2x + 1)) * 2.

So, the marginal cost function, MC, is given by MC(x) = 380 / (2x + 1).

To find the total cost of producing 170 units, we substitute x = 170 into the total cost function, C(x). So, C(170) = 1300 + 190 ln(2 * 170 + 1).

To find the marginal cost when 170 units are produced, we substitute x = 170 into the marginal cost function, MC(x). So, MC(170) = 380 / (2 * 170 + 1).